Acoustic Resonator

ABSTRACT

A resonator comprising a piezoelectric film which creates an acoustic path that is slightly longer in a central region of the resonator than at an edge of the resonator.

RELATED APPLICATIONS

The present application claims priority to U.S. Provisional ApplicationNo. 62/720,107 filed on Aug. 20, 2018, and U.S. Provisional ApplicationNo. 62/720,111, filed on Aug. 20, 2018, and incorporates both priorapplications by reference in their entirety.

FIELD

The present invention relates to resonators, and more particularly toaltering the shape or form of the resonator film.

BACKGROUND

Thin-film bulk acoustic resonators (FBAR or TFBAR) consist of apiezoelectric material sandwiched between two electrodes andacoustically isolated from the surrounding medium. FBAR devices usingpiezoelectric films generally resonate in the frequency range of 100 MHzto 10 GHz. Aluminum nitride (AlN) and zinc oxide (ZnO), with thicknessesranging from several micrometers down to tenths of micrometers, are twocommon piezoelectric materials used in FBARs.

BROADCOM™ (formerly Avago Technologies) is one of the leadingmanufacturers of FBAR devices. The main application of Avago FBARs is in4G cell phones and they are in extremely high demand. Avago FBARs are inAPPLE® and SAMSUNG® flagship products and there is not enoughmanufacturing capacity to satisfy the whole market demand. Avago isfocused almost entirely on producing FBARs for cell phones—to theexclusion of other, orthogonal markets. Domestic manufacturingcapability limits the availability of Avago FBAR.

Thus, there is a long-felt need for an improved FBAR.

BRIEF DESCRIPTION OF THE FIGURES

The present invention is illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings and in whichlike reference numerals refer to similar elements and in which:

FIG. 1A illustrates one embodiment of a side view of a simplified filmbulk acoustic resonator (FBAR) structure.

FIG. 1B illustrates one embodiment of a side view of a simplifiedsolidly mounted resonator (SMR) structure.

FIGS. 2A and 2B show an impulse simulation with a square FBAR resonator.

FIG. 2C illustrates the effects of wave diffraction by repeated aperturemasks.

FIG. 3A illustrates a simple model of a top hat electric field.

FIG. 3B illustrates a stress diagram, for the simple model of the tophat electric field of FIG. 3A.

FIG. 3C shows a more accurate model of the stress, based on Fouriercomponents ranging from the low wavenumber cutoff to the high wavenumbercutoff (resonator impulse response).

FIG. 3D illustrates a simple squared sum of the 10 lowest harmonics usedto construct the top hat function.

FIG. 3E illustrates the individual harmonics.

FIG. 3F illustrates a squared fundamental showing the variation ofresponse intensity.

FIG. 3G illustrates only the fundamental component of the top hatfunction.

FIG. 4A illustrates one embodiment of a ground state resonator.

FIG. 4B illustrates another embodiment of a ground state resonator.

FIG. 4C illustrates another embodiment of a ground state resonator.

FIG. 5A illustrates a lens embodiment of the focused resonator.

FIG. 5B illustrates another lens embodiment of the focused resonator.

FIG. 5C illustrates another embodiment of the focused resonator.

FIG. 5D illustrates one embodiment of the geometry of the acoustic beamwaist.

FIG. 5E illustrates one embodiment of the geometry of the resonator.

FIG. 5F illustrates one embodiment of using an added material having anincorporated layer with mismatched acoustic properties to achieve thethickening.

FIG. 6A illustrates one embodiment of a focused ground state resonator.

FIG. 6B illustrates one embodiment of the implantation pattern in thefocused ground state resonator.

FIG. 6C illustrates one embodiment of an implantation pattern in whichthere is implantation in the resonator film and the electrode.

FIG. 7A illustrates one embodiment of a cyclic axicon resonator.

FIG. 7B is one embodiment of the cyclic axicon pattern.

FIGS. 7C and 7D illustrate the impulse simulation of the cyclic axiconresonator.

DETAILED DESCRIPTION

The present invention discloses methods to improve acoustic resonatordesign, by altering the shape or form of the resonator film which isutilized. The improvement in one embodiment may be based on doping theresonator film, in one embodiment. The improvement in another embodimentmay be based on depositing additional material on the resonator film tocreate a convex or concave structure, in one embodiment. The improvementin another embodiment may be based on etching or depositing a pattern inthe resonator film stack. In one embodiment, the deposited pattern oretching creates a structure similar to the diffractive embodiment of anoptical axicon lens.

The following detailed description makes reference to the accompanyingdrawings in which like references indicate similar elements, showing byway of illustration specific embodiments of practicing the invention.Description of these embodiments is in sufficient detail to enable thoseskilled in the art to practice the invention. One skilled in the artunderstands that other embodiments may be utilized and that logical,mechanical, electrical, functional and other changes may be made withoutdeparting from the scope of the present invention. The followingdetailed description is, therefore, not to be taken in a limiting sense,and the scope of the present invention is defined only by the appendedclaims.

Glossary

FBAR: Film bulk acoustic resonator, consisting of a piezoelectricmaterial sandwiched between two electrodes and acoustically isolatedfrom the surrounding medium. FBARs include resonators isolated bysuspension over a void and resonators isolated by being positioned overa reflector (SMR). FBAR devices using piezoelectric films generallyresonate in the frequency range of 100 MHz to 10 GHz.

Q factor: Quality factor is a dimensionless parameter that describes howunder-damped an oscillator or resonator is, as well as characterizes aresonator's bandwidth relative to its center frequency. Higher Qindicates a lower rate of energy loss relative to the stored energy ofthe resonator; the oscillations die out more slowly. A pendulumsuspended from a high-quality bearing, oscillating in air, has a high Q,while a pendulum immersed in oil has a low one. Resonators with highquality factor have low damping so they ring longer. The bandwidth of aresonator can be defined in terms of its Q as: Δf=f₀/Q.

Acoustic resonator: An acoustic resonator, or bulk acoustic resonator,is a device consisting of piezoelectric material sandwiched between twoelectrodes that is acoustically isolated from the surrounding medium.FBARs are employed as radio frequency (RF) filters in cell phones andother wireless applications. Such filters made from a network ofresonators and are designed to allow only specific frequency ranges tobe received or transmitted.

Fourier Transform: The Fourier transform decomposes a signal that is afunction of time into the frequencies that make it up. The equationdefining a Fourier Transform is for any real number

:

F(

)=∫_(−∞) ^(∞) f(x)e ^(−2πix)

dx

-   -   where the independent variable x represents time, and the        transform variable        represents frequency.

Top Hat Function: A “top hat” function, over an interval from −L to +L,can be constructed (neglecting normalization) by summing an infiniteseries of the form:

$y = {\sum\limits_{n = 1}^{\infty}\; {\frac{\left( {- 1} \right)^{n - 1}}{\left( {{2n} - 1} \right)}{\cos \left( {\left( {{2n} - 1} \right)\pi \frac{x}{2L}} \right)}}}$

Where L is the length of the “top hat” function and n is the nthharmonic of the series. Note that the “top hat” centered about x=0 isonly composed of odd harmonics because it is a symmetric function (hencethe (2n−1) representation that transforms the index, n, to only oddnumbers from +1 to infinity). An approximate top hat function can beconstructed by summing a subset of the harmonics. FIG. 3C illustrates asimple squared sum of the 10 lowest harmonics used to construct a tophat function. FIG. 3D illustrates the individual harmonics themselves.Note that the “top hat” function as defined here is truncated to zerofor values of x less than −L and more than +L. In other words, it is thefunction above multiplied by 1 for −L<=x<=+L and multiplied by 0 for|x|>L.

Acoustic lens: An acoustic lens is a structure that imparts a relativedelay to some portion of an acoustic wave's wave front. In the case of a“converging”, or “convex” lens the material in the lens' central regionhas a lower sound speed or is thicker than the surrounding lensmaterial. Conversely, in the case of a “diverging”, or “concave” lensthe material in the lens' central region has a higher sound speed or isthinner than the surrounding lens material. This effect may be referredto as “acoustic lensing.”

Overview

The FBAR is the enabling technology of 4G cell phones, as the SAW filterwas the enabling technology of analog cell phones. In most cases, suchresonators are suspended over a void but solidly mounted resonator(SMRs) may also be used. The purpose of FBARs in the data communicationselectronics of cell phones is to discriminate adjacent data channels (infrequency space). The more selectively the data channels can bediscriminated, the more channels may be used in a given cell phone band.One limiting factor in how many data channels may be used is thequality-factor, or “Q”, of the FBARs used as channel filters. The higherthe Q, the narrower the channels that may be defined, and the more ofthem that may be fit into a given RF transmission or receptionbandwidth. Presently, a typical cell phone has 10 to 20 FBAR devices.These FBARs are used to define the data channels.

There are several immediate benefits to narrowing the data channelspacing: better data performance for the user because more data channelscan be utilized, and more FBAR sales by the manufacturer in proportionto the number of data channels. The Q improvement depends on resonatorsize. Therefore, a further benefit of improving the Q of a givenresonator is that the resonator can be reduced in size while maintainingor even improving its Q value, compared to prior designs. This increasesthe number of devices that can be made on a single wafer, increasesproduction, and reduces cost. Thus, improving FBAR device Q isadvantageous.

The reason that an oscillator has a finite Q is (mostly) that in real,physical systems there are always energy loss mechanisms. The Q of anoscillator system can be defined through its rate of energy loss as:

$Q = {{2\pi*\frac{{Energy}\mspace{14mu} {Stored}}{{Energy}\mspace{14mu} {Lost}\mspace{14mu} \left( {{Per}\mspace{14mu} {cycle}} \right)}} = \frac{{Energy}\mspace{14mu} {Stored}}{{Energy}\mspace{14mu} {Lost}\mspace{14mu} \left( {{Per}\mspace{14mu} {radian}} \right)}}$

FBAR devices are prone to energy loss due to various mechanisms. One ofthe most significant is mechanical coupling to their substrate. Otherenergy loss mechanisms include resistive losses in the electrodes andmechanical (acoustic) losses in the piezoelectric and other materials inthe FBAR “stack”. Reducing the effect of the worst of these lossmechanisms would improve the Q.

There are two main ways to reduce the energy losses into the substrate:by suspending the FBAR over a pit so that its bottom face is not incontact with anything, or by building the piezoelectric film over anacoustic reflector (SMR). For the purposes of this discussion, the term“FBAR” encompasses both types of resonators. In practice, the SMR seemsto be inferior to the suspension method in its ability to isolate theresonator structure because it has losses into the acoustic reflector inaddition to losses to its edges similar to suspended designs.Additionally, by shaping the piezoelectric film in such a way thatacoustic energy does not get directed to the edges of the resonator, andfrom there into the substrate, energy loss can further be reduced.

The substrate losses in an FBAR suspended over a void are only at theplaces where the FBAR physically contacts the substrate, generally theFBAR's perimeter. Typically this leads to FBAR Q having roughly anarea/perimeter relation (Larger devices tend to have higher Q). In thecase of SMR devices the entire resonator film is in mechanical contactwith the substrate via the reflector stack but the purpose of thereflector is to acoustically decouple the bottom face of the resonatorfrom the substrate. However, even though the edges of an SMR may bemechanically detached from the substrate, an SMR may still have theunwanted behavior of excessive spurious modes caused by acoustic wavestraveling tangent to its surface. Additionally, in the case of an SMRwithout edge coupling to the substrate the spurious modes canpotentially be much larger than in a similar FBAR.

FIG. 1A illustrates one embodiment of a simplified FBAR 100 structure.In this embodiment, the piezoelectric film 110 is suspended over a void,or pit 120. The film 110 has conductive electrodes 130 on the top 130Aand bottom surfaces 130B to provide electrical field coupling to thefilm 110 and to define the shape of the resonator's outline. The portionof the film 110 between both the bottom and top electrodes, is theregion 160 under piezoelectric stress.

FIG. 1B illustrates another embodiment of a simplified FBAR structure,in which the piezoelectric film is built over a reflector, rather than apit or void. Such devices are referred to as solidly mounted resonator(SMR). An SMR, or solidly mounted resonator is similar to an FBAR exceptthat it utilizes an acoustic reflector in place of an undercut isolationvoid. In one embodiment, the reflector is an acoustic Bragg reflectorstack. Although the below illustrations use the FBAR structure with avoid, the present improvements to FBAR structures may be utilized witheither structure.

A simple version of an FBAR is constructed as a stack of planar layersof material. The resonator 150 itself is composed of the top electrode130A, a layer of piezoelectric material 140 and a bottom electrode 130B.In one embodiment, the piezoelectric material 140 is aluminum nitride(AlN) or zinc oxide (ZnO).

The resonator 150 is built with a cavity 120 (or reflector 125, if anSMR) beneath it and it is attached to the silicon substrate 180 only atits edges. In one embodiment, the cavity 120 is made using a chemicaletching process through one or more vias cut in the AlN layer. Since theresonator 150 is constructed over a cavity 120 only its edges canmechanically couple to the substrate 180. If care is taken to design theresonator materials to be low loss (mechanically very homogeneous andstiff, and the electrodes and interconnects very conductive) then theonly significant losses will be at the resonator edges in contact withthe substrate.

How much energy actually gets to the edges depends on how well waves canbounce back and forth across the surface of the FBAR 100, and thatdepends on the shape of the resonator. A square is bad choice for adesign due to its high degree of symmetry and parallel sides. Waves canreflect back and forth across the surface of the square and build up tosignificant amplitude via constructive interference. In one embodiment,the FBAR structure utilizes an irregular pentagon or other asymmetricpolygon with irrational length ratios. The length of each side varies,to reduce reflections.

FIGS. 2A and 2B show an impulse simulation with a square FBAR resonator.The presence of the pronounced “banded” structure is evidence ofconstructive interference.

FIG. 2C illustrates the effects of wave diffraction by repeated aperturemasks. This shows the evolution of transverse (spurious) mode structure.The example shown here is a series of repeated square apertures spacedat twice the (effective) acoustic film thickness. This example modeledan SMR structure, so the bottom surface of the resonator did not have anaperture mask but the top surface did (the top electrode outline). Waveenergy diffracted to the edge of the aperture was assumed to be lostinto the device substrate. The number shown is the nth aperture. The 1stframe contains the initial distribution of impulse energy and allfollowing frames contain the repeated diffractions from the device'sedges. Modeling the standing wave in the resonator as a traveling wavein a “stack” of identical resonators facilitate physical insights.

An analogy that may explain why this modeling is used, is a long hallwaywith door-less door frames set at repeating intervals such that a persontraveling straight down the hallway would pass through every frame.There is a bit of position uncertainty, or fuzziness, in the location ofthe person traveling the hallway. The traveler's position uncertaintymakes it impossible for the them to “cleanly” pass through the doorframes without being slightly deflected by the frames. As the travelerprogresses down the hallway they accumulate an uncertainty in theirdirection of travel because of their repeated, though (initially) weak,interaction with the frames. As their direction of travel becomes lessand less straight along the hallway, their interactions with the doorframes become more and more strong. Eventually the traveler's directionof travel becomes so scrambled that collisions with the frames dominatetheir motion. Obviously, minimizing the interactions with the doorframes is important for the traveler to make it farther along thehallway.

In the “hallway analogy” the hallway and door frames are in a lineararrangement that is traversed only once by the traveler. It isequivalent to, though easier to understand, a similar analogy whereinthe hallway is replaced by a single segment of hall, a “room”, with doorframes on each end containing “reflectors” that would cause a travelerprogressing to a door frame to have the component of their motion alongthe hall reversed (like “ball bouncing off wall”). In this analogy, thetraveler would “bounce back and forth” between the reflectors in theframes in the little “room”. However, the traveler would still have theweak position uncertainty, as in the hallway analogy above, that wouldcause (initially) weak interactions with the door frames, and anaccumulation of uncertainty in their direction of motion. Eventually thetraveler's motion would become just as scrambled as in the hallway,although it would be more difficult to understand why because thepresence of “reflectors”, and the back-and-forth motion of the travelerwithin the room in the description provide distractions to theimagination.

One approach is to model the standing wave in the resonator as atraveling wave in a repeating “stack” of identical resonators, much likeusing the “hallway” description instead of the “room” description. Thetwo are equivalent, though they facilitate differing sets of physicalinsights. FIG. 2C's simulation utilizes this analogy.

Another method of reducing the energy that gets lost at the resonatoredges is to suppress the harmonics that are introduced as a consequenceof driving the entire resonator surface. In standard resonators, thedriving force across the film of the resonator is a constant from onearea to the next (constant stress) because the electric field betweentwo parallel plane electrodes is a constant (except at the edges).

The stress induced in an FBAR's film is a function of the electric fieldapplied and the material's piezoelectric response to the field. In thecase of FBAR devices the RF electric field tends to be spatially aconstant throughout the bulk of the material between the top and bottomelectrodes. One way of representing the mode structure of waves inducedby the electric field is a Fourier analysis of the driving field. In thecase of a typical applied RF electric field that is a constanteverywhere between the top and bottom electrodes, and zero everywhereelse, we can use the Top Hat function and study the resulting Fourierwave components. The top hat function is zero outside a specified range,and of constant, finite value within the specified range Typically thefunction is normalized so that the product of its length and amplitudeis unity.

In the FBAR 100 shown in FIG. 1A, the electric field (and resultingmaterial stress) is constant in the bulk of the material between theelectrodes and falls promptly to zero outside the region of theelectrodes. This can be represented as shown in FIG. 3A, showing thesimple model of a top hat electric field. Since the response of thepiezoelectric film is modeled as linear and proportional to the appliedelectric field, the stress induced in the material should be a constantbetween the electrodes and fall to zero outside the electrodes, as shownin FIG. 3B.

The Fourier components in the (impulse) response generally should notinclude wave components that have higher frequencies than the resonancebeing driven in the bulk material. Unless the film is being driven intohigher order modes of excitation than the fundamental, such as bynon-linear effects, the shortest wavelength (the high wavenumber cutoff)that the Fourier synthesis ought to contain is, roughly, twice theacoustic thickness of the FBAR. The longest wavelength (the lowwavenumber cutoff) that the Fourier synthesis can contain is twice theacoustic length (or width) of the FBAR device. Thus, a finite range ofwaves add up and represent the material's response to the drivingelectric field. This analysis ignores non-linear effects.

FIG. 3C shows a more accurate model of the stress, based on Fouriercomponents ranging from the low wavenumber cutoff to the high wavenumbercutoff. The response is calculated by summing the Fourier components ofa top hat function in the range between the low and high wavenumbercutoffs and then squaring the resulting synthesized function. The rapidfluctuations in amplitude near resonator edges become apparent in thismodel.

The energy transfer to the FBAR device edges is dependent on thequantity, spatial frequency, and amplitude of the harmonics. Reducingthe presence of those harmonics will prevent them from constructivelyinterfering and building up to transport significant energy. There canbe significant spatial modulation to the response of a spatiallyconstant, but time varying, (electric field) stimulus due to thepresence of a finite upper bound to the frequency of the Fouriercomponents available to construct the actual response.

Having only the few lowest harmonic components available to construct anapproximate top hat function leads to the seemingly undesirable resultof having large spatial fluctuations in the response function. However,the energy transport depends on the product of the synthesizedfunction's intensity variation and how rapidly the variations occur.Thus, even large variations away from an ideal top hat function in theintensity of the resulting waveform do not necessarily indicate largeenergy transport. The energy transport to the edges of the device maystill be small if the waveform varies slowly in space. In the limit ofapproximating the top hat using only the first order harmonics, shown inFIG. 3F, the fundamental component of the top hat function shown in FIG.3G, something interesting happens: The rate of variation of responseintensity is held to a minimum, thus the energy transport to the edgesof the response field (device edges) is minimized.

Therefore, having a planar resonator structure that has a constant tophat stress distribution across its surface is a poor way to make a lowloss resonator. In one embodiment, variations of the design that can beused to create a spatial stress distribution in the resonator that issimilar to figure the fundamental component of the top hat functioninclude:

-   -   Ground State resonator    -   Focused Resonator    -   Focused Ground State Resonator    -   Cyclic Axicon Resonator

Embodiments of the Improved FBAR Ground State Resonator

This design takes advantage of the fact that the intensity of theelectric field within the piezoelectric film is tapered if the electrodedoes not extend all the way to the edges of the film, and is alignedwith the film's piezoelectric axis.

FIG. 4A illustrates one embodiment of a ground state resonator 400 inwhich the pit 440 beneath the piezoelectric film 410 is fairly deep, andthe bottom electrode 430 is placed on the bottom of the pit 440. Thebottom electrode spans only a portion of the resonator to create atapered electric field towards the resonator's edges and a strongerfield towards its center. This illustration shows the non-uniformelectric field.

FIG. 4B illustrates an alternative embodiment of the ground stateresonator FBAR 450 in which the bottom electrode 480 is on the bottom ofthe substrate 470, with an insulating and low loss substrate.

FIG. 4C illustrates one embodiment of the ground state resonator of FIG.4B, utilizing an oxide wafer. An Si device layer 496 is used to supportthe resonator film. When the pit is etched, the etch, stops on the oxidesubstrate 498. The bottom electrode 499 is positioned on the back sideof the oxide substrate 498.

In ground state resonators, the bottom electrode 480 is a smaller sizethan the film 410. This would cause a considerable fringing of theelectric field toward the edges of the resonator. The effect of thefringing field would be to reduce the electromechanical response of thepiezoelectric film near its edges. By tailoring the response of the filmto more nearly match an (idealized) half-cosine shaped deflection, thehigher frequency modes tangent to the resonator's surface would bereduced. This would reduce energy transport to the device's edges andimprove Q factor.

However, there are drawbacks to any embodiment that moves the top orbottom electrodes farther away from the piezoelectric material. The mostimportant drawback being that the intensity of the electric fielddriving the piezoelectric material is inversely proportional to thedistance between the electrodes.

Focused Resonator

The acoustic wave may be focused by shaping the resonator, to create atapered convex area in at least a portion of the resonator. The shapingis to modify the acoustic thickness of the resonator so that it formsmore of a convex (or concave) lens than a flat, parallel platestructure.

FIG. 5A illustrates one embodiment of the focused resonator. A convexstructure 520 is formed on top of the resonator 510. In one embodiment,the convex structure 520 is positioned over the top electrode. The topelectrode 515 may be located on top of the convex structure 520, in oneembodiment.

In another embodiment, the convex structure 530 may be formed bythickening the central portion of the resonator 540, as shown in FIG.5B. In one embodiment, the convex structure 535 may be formed byadditional deposition of material in the central portion of theresonator. In one embodiment, such deposits may be tapered, forming aconvex area. In one embodiment, thickening the resonator 540 like a lenscauses the resonator 540 to behave like a lens, and focus the acousticpower away from the edges. In one embodiment, thickening could beaccomplished by the sputter application of additional piezoelectricmaterial through an aperture mask. Alternative methods of forming such ashape in the resonator may be utilized, including etching or depositionof additional material layers.

In one embodiment, the additional material thickness can be a few atomiclayers or less such as a fractional atomic layer by using a sparsepartial coverage of atoms in the resonator center.

In another embodiment, as an alternative to thickening the centralportion of the device, the edges of the device may be thinned instead.In one embodiment, thinning could be accomplished by ion milling or someother etching technique (wet or dry) that allows for appropriate spatialselectivity so that only the portions of the device that requirethinning are subject to etching. Either method, of adding material orsubtracting material, would be equivalent since the end result is aconvex (or concave) lens shape with respect to the acoustic thickness ofthe device. However, there may be advantages in adding or subtractingmaterial that depend on device design and which one is used will dependon details of design and available manufacturing processes

FIG. 5C illustrates another embodiment of the focused resonator in whicha stiffening electrode structure is included in the device's “materialstack.” The stiffening electrode structure 555 provides a DCelectrostatic bias field to the device's edges. The component of theapplied DC field normal to the device's plane would pre-load thepiezoelectric material of the resonator 560, causing it to stiffen andhave a slightly higher sound speed (or in the case where a diverginglens is desired the resonator electrodes could have a DC bias impressedon them with the addition of an additional edge field imposed to reducethe overall field at the edges). This local stiffening would cause theregions under stress to have a shorter acoustic path and the regions notunder stress, near the device's center, to have a longer one, eventhough the physical thickness of the film is constant. This embodimenthas the advantage of being electrically adjustable for tunable devicebehavior. However, it does require a stable bias voltage to adjust thefocus.

The focused resonator's principle of operation is to create an acousticpath that is slightly longer in the resonator's central region than atits edges. This causes the wave front in the resonator to have itscurvature corrected to reduce spreading energy into the substrate at theresonator's edges by diffraction. In general, for a given wavelength andresonator size, the acoustic path will be lengthened by theapproximately same amount, regardless of whether the lengthening is doneby changes in material thickness, stiffness, or other means.

In one embodiment, the added thickness is based on considerations ofwave front diffraction. The criterion for suppressing diffractive lossesinto the substrate is that there be a correction to the curvature of thewave front propagating within the resonator that is opposite to thecurvature induced by diffraction. In this way, the wave front remainsnormal to the surface of the resonator and does not propagate energy tothe resonator's edges.

If the wave within the resonator is treated as a traveling wave insteadof as a wave reflected between the resonator boundaries then a proceduresimilar to the standard one for finding the divergence of a Gaussianbeam waist may be employed. The curvature of the wave fronts is zero atthe beam waist and also approaches zero as z→±∞. It is equal to 1/Rwhere R(z) is the radius of curvature as a function of position alongthe beam, given by

${R(z)} = {z\left\lbrack {1 + \left( \frac{z_{R}}{z} \right)^{2}} \right\rbrack}$

where the beam waist is w₀, and z_(R) is the Rayleigh range. FIG. 5Dshows the geometry of the beam waist.

Thus, after substitutions of setting the beam waist to the resonatordiameter, w₀=d, the Rayleigh range, z_(R)=πw₀ ²/λ, and setting z=λ/2(for a half wavelength thick resonator), the geometry of R(z) is:

${R(z)} = {\frac{\lambda}{2}\left\lbrack {1 + \left( \frac{2\pi \; d^{2}}{\lambda^{2}} \right)^{2}} \right\rbrack}$

The equation for solving for the curvature at a distance of thethickness of the resonator, or half a wavelength, from the beam waist isused to calculate the added thickness. That is to say, the beam waist ispositioned on the bottom surface of the resonator and the calculationsdetermine the curvature of the wavefront at the top surface. Thecalculations are concerned with the wavefront very close to the beamwaist (very closely in the diffractive near field). Once the curvatureis calculated, and given the size of the resonator, the distance neededto add to the acoustic path length in the center of the resonator can bedetermined.

Given the curvature of the wavefront at a given distance from the beamwaist we can use simple geometry to find the added thickness, Δz.

Δz=R−R cos θ≈R−R(1−½θ²+ . . . )

Using the small angle approximation of θ=(d/2)/R

${\Delta \; z} \simeq \frac{d^{2}}{8R}$

To simplify R(z), we note that the 1 inside the brackets contributeslittle in the case where z_(R)>>z, so by eliminating that:

${R(z)} = {\frac{\lambda}{2}\left( \frac{2\pi \; d^{2}}{\lambda^{2}} \right)^{2}}$${{{For}\mspace{14mu} z} = {\lambda \text{/}2}},{{\Delta \; z} \simeq \frac{\lambda^{3}}{16\pi^{2}d^{2}}}$

Using this equation to calculate some examples shows that the addedthickness is easily added. For f=2.5 GHz, λ=4 μm (assuming AlN), andd=100λ/2=200 μm, Δz≅1.0×10⁻¹¹m=0.01 nm=0.1 Angstroms. f=600 MHz, A=16.7μm (assuming AlN), and d=400 μm, Δz≅1.8×10⁻¹° m=0.18 nm=1.8 Angstroms.

Thus, the added thickness of a few atoms in the center of an FBAR mayimprove its Q by a significant amount. The added thickness does not haveto be a continuous sheet of AlN (or electrode material or other materialin the device stack) molecules. In one embodiment, it can be a sparsedensity of molecules that is only a partial monolayer and stillcontribute to a change in acoustic thickness that is on-average afraction of a molecular layer thickness. In one embodiment, the addedmaterial could be composed of additional incorporated layer withacoustic properties, that is neither of the resonator nor of theelectrode structure. In one embodiment, such added material may have anacoustic mismatch such that the layer could be physically thicker thanwhat is indicated by the above formulae but that nevertheless introducesa similar phase delay to that which would be introduced by the verysmall thickness change described by the formulas above. In oneembodiment, the relationship of the thickness of the material that maybe incorporated may depend on the acoustic properties of the material.

FIG. 5E illustrates one embodiment of the geometry of the central areaof the resonator, showing the dimensions of the relative thickening ofthe resonator material. The relative thickening may be achieved byadding extra material at the center area, or by thinning the edge area.The material added to thicken the central portion of the resonator inone embodiment would be of the same form as that shown in the existingFIGS. 5A and/or 5B, except that the added thickness would be greater(physically thicker) but the acoustic wave extending into the addedmaterial would be of much reduced amplitude because the mismatchedmaterial would acoustically couple only minimally to the resonatorstructure itself.

In one embodiment, the resonator could be thinned toward its edges toproduce the convex shape. The thinning could be accomplished eithermechanically by etching or milling, in one embodiment. In oneembodiment, the thinning may be achieved by passively stressing thepiezoelectric material using ion implantation as described below or byactively stressing the piezoelectric material by use of a non-uniformelectrostatic field, as discussed above.

Any method that causes a variation of acoustic thickness across theresonator will result in some spreading of the device's resonantfrequency—because the device's resonant frequency is determined by itsacoustic thickness. However, care must be taken in the optimization ofthe design. There is an implicit tradeoff between Q improvement due tothe amount of energy loss reduction from focusing and the reduction in Qfrom spreading the resonator's operating frequency over a broaderbandwidth. However, a 2.5 GHz resonator with very low mass electrodeswill have a film thickness of about d=v/2f=2 μm. If the variation inthickness is a few atomic layers, say half a nanometer, then thebandwidth broadening only a few tenths of a part per thousand. Thatseems to provide a Q limit of:

$Q \precsim \frac{2\pi}{0.5*10^{- 3}} \approx 10^{4}$

due to bandwidth broadening from thickness variation. Since current bestdevices have a Q well under 10,000 this broadening is relatively minorcompared to the benefit derived from the shaping of the resonator.

The resonator will automatically seek out the resonant frequency withthe least losses. Hence, the low frequency portion of the resonancewould be preferred by the resonator itself because that would have thewave propagating farthest from the device's edges. If an impulseresponse is provided to the resonator the frequencies with the lowestlosses will persist the longest and have the most gain applied to themby the resonator's feedback amplifier electronics. Thus, portion of theresonance corresponding to the resonant frequency range of the device'scenter will dominate. However, in one embodiment, this effect may bereinforced by electronically pulling the resonator's drive frequencyslightly towards the lower shoulder of its operating band. The FBAR canpreferentially drive the portion of the resonance that is matched to thecentral, lower frequency, portion of the shaped resonator structure.This technique improves the device's performance by effectivelymodifying its response to be larger in the center than at the edges.This will result in a response biased towards the half cosine of FIG.3E, and away from the top hat response of FIG. 3A. By adjusting thedrive frequency, the system mitigates the loss of Q from resonatorbandwidth spreading brought on by the variation in device thickness(convexity) and provides additional mitigation against energy losses atthe resonator edges by reducing the stimulation of the resonator edgesby way of resonant mismatch.

Focused Ground State Resonator

Another way to tailor the device piezoelectric material's response to anapplied electric field is to implant ions in the device's piezoelectricmaterial near the resonator's edges. This changes the physicalproperties of the material. In one embodiment, the implantation would beperformed after the resonator piezoelectric material was constructed butprior to creation of the FBAR. In another embodiment, it may be possibleto stiffen the electrode structure instead of the piezoelectric materialof the FBAR since the acoustic wave within the device transits throughthe electrodes as well as the piezoelectric material. Local alterationsof the acoustic path length are somewhat agnostic to where along theacoustic path the alteration happens. For example, ion implantation maybe used for stiffening of metals.

Obviously, stiffening of the electrode structure, instead of thepiezoelectric material, would leave the piezoelectric response of thedevice unaltered from its ordinary, uniform response. There may bedesign advantages to stiffening without modifying the piezoelectricresponse. Alternatively, if more alteration to the piezoelectricmaterial is desired than would be the case for acoustic focusing alone,it may be advantageous to “over-expose” the ion implantation in someareas of the piezoelectric material, and implant ions in the centralportion of the electrode structure to compensate. For example, the ionimplantation may be overexposed near the edges of the resonatorpiezoelectric material and then additional ions may be implanted in thecentral portion of the electrode structure. There may be designflexibility allowed by separate ion implantation patterns to both thepiezoelectric material and the electrode structures.

In one embodiment, the process lays down a uniform film on a uniformsubstrate and then post process the film layer. In one embodiment, theconcentration of implanted ions would be approximately zero in thecentral area of the resonator, and then have a number density such thatit progressively alters the material's piezoelectric properties towardthe device's edges, yielding a downward parabolic shaped piezoelectricresponse. This allows the use of a simple, planar electrode structurethat is familiar to FBAR construction and appropriate to device massfabrication on wafers. To be sure, it may be appropriate to vary theelectric field intensity as a spatial function as well as to tailor thematerial response.

An ion implantation gradient that rises in density as a function ofradius from the device's center also stiffens the piezoelectric materialleading to an upward change in the local speed that sound travelsthrough the material. Since the implantation would be greater near thedevice's edge the sound speed would be greater near the edge. Increasingthe sound speed is the same as reducing the acoustic thickness of thedevice material. This effective thinning of the acoustic thickness isused to construct a self-focusing effect to further constrain theacoustic energy away from the device's edges.

FIG. 6A illustrates one embodiment of a focused ground state resonator600. The resonator film 610 has a bottom electrode 625 and a topelectrode 620. The resonator 610 is positioned over a pit 630 in thesubstrate 635. The stippling 615 of the resonator film 610 shows oneembodiment of the implantation gradient of the ions. In one embodiment,the penetration depth is on the order of 1-2 μm. For resonatorsoperating below 1-2 GHz this may be accomplished by implantation in thetop portion of the film. In one embodiment, the system is flexible as toa concentration of ions—roughly the same total number of ions as wouldbe needed to stiffen the material all the way through, but with adensity concentration near the upper surface of the film. In oneembodiment, the ion density would be maximal at the stopping depth ofthe ions in the material, not at the top surface.

By selectively partially destroying the electromechanical response ofthe piezoelectric film of the resonator its response to a driving fieldapproximates the half-cosine function even when the film itself is ofconstant physical thickness and even when the electric field from theelectrode structure is uniform. The implanted ions disrupt the crystalstructure of the film that is so necessary for piezoelectric behaviors,stiffen the structure of the material by putting the ion implantedportion of the film under compressive stress, and may add an implantedelectric polarization to further enhance the compressive preloading byproviding an electric field that acts locally on whatever local portionsof the piezoelectric material that still retain the piezoelectricbehavior associated with an undisrupted crystal structure.

Spatially structured degradation of the piezoelectric material'sresponse to an electric field (and its ability to generate an electricfield) will cause the device's response to be closer matched to theground state, fundamental mode of resonance. The “fundamental mode” ofresonance of the very simple theoretical a 2-dimensional cross-sectionalslice through a three dimensional planar resonator structure (such asshown in cross sectional FIGS. 1A and 1B, where the dimension “stickingout of the page” has been suppressed) is the largest half-cosinefunction that fits between the edges of the resonator. It has thelongest wavelength of any of the modes. For planar resonators, the“fundamental mode” would be the lowest order harmonic mode of the2-dimensional structure (analogous to the half-cosine, but in more thana single dimension). The accompanying reduction in active acoustic modestangent to the device's surface will reduce energy transport out of theresonator structure and improve its Q factor. The active acoustic modesrefer to the energy content of available vibration modes.

Note that the simplified structures shown here show a time slice througha resonator structure, rather than the exact response of a resonatorthat is an actual planar structure. The depiction is of a 2D crosssectional slice through a 3D, planar structure. This suppresses theportion of the stress/deflection (response) pattern that “sticks out ofthe page”, leaving only a 2D depiction of the response. However, sincethe thickness of the resonator is treated as if it were one slice in arepeating structure (the hallway analogy above), with the acoustic wavepassing in one direction, rather than bouncing back and forth, it iseffectively a “time” dimension, not a space dimension. The deflectionpattern is not a cosine function in only 1D, but is a product of twofunctions, one “across the page” and one “in/out of the page”.

The complete response of a planar resonator depends on thethree-dimensional resonator shape. For example (when viewed from thetop), a square resonator will have a cosinusoidal function along itswidth multiplied by a cosinusoidal function along its height. In crosssection, one of the cosine functions is selected as representative. Acircular resonator structure will have a Bessel mode structure as itsresonant modes, not cosines. Thus, a slice through a square gives arealistic solution to the response along the cross-sectional portionshown but a slice through a circular resonator will not havecosinusoidal modes as its response. Instead the response will looksomewhat like a cosine function, big in the center and zero at theedges, and it'd be analogous to the lowest order mode of a square, butit is not exactly the same thing. Thus, while the side-view crosssection of a square resonator is indistinguishable from the side-viewcross section through a circular resonator the modes in either would bedifferent because of the shape of the material being suppressed in thediagram.

Spatially structured compressive preloading of the piezoelectricmaterial using ion implantation increases its mechanical stiffness andincrease the speed sound travels through the material. The increase inlocal sound speed acts to decrease the local acoustic distance in thematerial, causing its acoustic shape to be convex lens-like in the ionimplanted regions of the resonator film.

In one embodiment, spatially structured implantation of ions withcomplimentary charges in the upper and lower volumes of thepiezoelectric material can be used to place the nearby material in alocally generated electrostatic field.

FIG. 6B illustrates one embodiment of the ion implantation pattern 680.If the piezoelectric material subject to this implanted electrostaticfield has not had its electromechanical response completely destroyed bythe implantation process then it will be caused to be under tensile orcompressive stress—to extend or contract—due to the applied (implanted)electrostatic field. The placement of the implanted ions in the upperand/or lower portions of the material will affect whether the resultingelectrostatic field is oriented along or against the axis ofpiezoelectric activity of the material. A proper arrangement ofimplanted ions can be used to place the material under compressivepiezoelectric action, enhancing the compressive effects of the ionimplantation and improving the behavior of the resulting acousticlensing. For example, implanted positive ions that provide positivecharges embedded in the AlN film's top portion will establish anelectric field directed downward, through the AlN, to the ground planeunderneath. If the orientation of the AlN film is such that the embeddedelectric field causes the film to piezo-electrically contract then thefilm will be very slightly stiffer, compared to regions not subject tothe embedded electric field, due to preloading. Conversely, ionsimplanted so that the resulting embedded electric field causes thepiezoelectric material to expand will also preload the film by puttingit under tensile, rather than compressive, stress. There will bedifferences in the behaviors of tensile vs. compressive preloading thatmay lead to advantageous tailoring of film and device behavior. FIG. 6Cillustrates an alternative implantation approach, in which ionimplantation is applied to the resonator as well as the electrode. Theelectrode in this illustration is shown thicker to allow theillustration of an exemplary implantation pattern. Note that the portionof the resonator under the electrode has ion implantation as well. Inone embodiment, this design utilizes separate ion implantation for theresonator and the electrode.

Cyclic Axicon Resonator

FIG. 7A illustrates one embodiment of a cyclic axicon resonator. Oneembodiment of the “Cyclic Axicon” resonator 700 design consists of anetched pattern of rings 730 on the device's top electrode 720. Etchingthe top electrode 720 gives the sharpest, most vertical sidewalls to theresulting “corrugation” structure, which has the sharpest contrast stepin the resulting acoustic structure. In cases where a sharp step inthickness gives an advantageous diffractive pattern this may bedesirable. Other ways of creating the pattern of rings may be used, suchas material deposition, cutting, ion implantation to stiffen and modifythe piezoelectric material or modify stiffness of the electrodestructure, or other methods. These methods may give a more gradualchange in acoustic depth of the axicon rings, leading to a differentdiffractive behavior with different advantages than those generated byan axicon mask with sharp steps of depth.

The depth of etching for the circular “corrugations” 730 is a few tensof nanometers for resonators with multi GHz operating frequency toperhaps over a micron for resonators 710 with sub-GHz operatingfrequency. The depth of etch relative to the resonator film thicknessdetermines the contrast of the resulting diffractive acoustic element,thus has an effect on how strongly the acoustic wave in the resonator isconverted into a Bessel beam-like configuration. The spacing of thecircular corrugations is lithographically matched to the naturaloperating frequency of the resonator. Thus, in one embodiment, eachresonator of a particular size and thickness may have structureoptimized in ring spacing and ring depth to match.

FIG. 7B illustrates an exemplary cyclic axicon mask, used the impulsesimulations illustrated in FIGS. 7C and 7D. As can be seen, after thesteady state pattern shown in FIG. 7D develops it is essentiallyunchanging, indicating very low coupling to the outside environment.

In one embodiment, the known circular FBAR problem of mechanicalmembrane rupture in the center may be addressed by this design. Themechanical rupture is caused by the tendency for a divergence in thepower per unit area of the Bessel function at its center. For example,in the case of Bessel beams, each of the ring-like structures of thebeam carry an equal amount of power and the power density of the centralspot is therefore high. In one embodiment, this may be addressed bymodifying the height of the central portion of the circular corrugationssuch that the power is deflected slightly away from the center of thestructure. In one embodiment, the axicon mask (ring set) may be appliedto non-circular resonator shapes, such as a resonator in the irregularpentagonal shape.

A variation of the Cyclic Axicon Resonator design could use thediffraction structure of a spherical wave front intersecting with aplane instead of uniformly spaced, concentric rings. Such a diffractionpattern is known as Newton's Rings or a continuous zone plate or astepped zone plate. The diffraction pattern is similar to the cyclicaxicon pattern shown in FIGS. 7A-7D, with a non-uniform spacing of therings. The spacing of the rings is defined by the wavelength of thewaves they are constructed from, and the focal distance they areintended to reproduce. A Newton's Rings variation of the diffractivedesign is used as a method of imparting an acoustic curvature to theresonator surface that is similar to that caused by a spherical surface.Other variations of diffractive structures comprised of acoustic speedvariations may be used.

In the foregoing specification, the invention has been described withreference to specific exemplary embodiments thereof. It will, however,be evident that various modifications and changes may be made theretowithout departing from the broader spirit and scope of the invention asset forth in the appended claims. The specification and drawings are,accordingly, to be regarded in an illustrative rather than a restrictivesense.

I claim:
 1. A resonator comprising: a piezoelectric film which createsan acoustic path that is longer in a central region of the resonatorthan at an edge of the resonator.
 2. The resonator of claim 1, where theresonator is shaped using one or more of: depositing, etching, milling,and actively stressing the resonator.
 3. The resonator of claim 1, wherethe resonator is shaped by implanting ions in near edges of theresonator.
 4. The resonator of claim 3, wherein the ions are implantedprogressively toward the edges of the resonator.
 5. An acousticresonator comprising: a substrate; a pit in the substrate, the pithaving an edge; a resonator film positioned over the pit and touchingthe substrate on the edge, the resonator film including a top electrodeand a bottom electrode, the resonator film having an acoustic path thatis longer in a central region of the resonator film than at an edge ofthe resonator film.
 6. The acoustic resonator of claim 5, wherein theresonator film comprises a piezoelectric material which is one of:aluminum nitride (AlN) and zinc oxide (ZnO).
 7. The acoustic resonatorof claim 5, wherein a top electrode is on a top surface of the resonatorfilm, and the bottom electrode is on a bottom surface of the resonatorfilm, the bottom surface facing the pit.
 8. The acoustic resonator ofclaim 5, wherein a top electrode is on a top surface of the resonatorfilm, and the bottom electrode is on a bottom surface of the substrate,below the pit.
 9. The acoustic resonator of claim 5, wherein a topelectrode is on a top surface of the resonator film, and the bottomelectrode is at a bottom of the pit.
 10. The acoustic resonator of claim5, further comprising: an acoustic Bragg reflector stack positioned inthe it in the substrate, below the resonator film.
 11. The acousticresonator of claim 5, further comprising: a lens structure on a topsurface of the resonator film, below the top electrode, the lensstructure thickening a portion of the resonator film.
 12. The acousticresonator of claim 11, wherein the lens structure is convex.
 13. Theacoustic resonator of claim 5, further comprising: stiffening electrodeson edges of the resonator film to stiffen the edges of the resonatorfilm.
 14. The acoustic resonator of claim 5, wherein the resonator has anon-uniform response to resonation, with a reduced flexibility at edgesof the resonator film.
 15. The acoustic resonator of claim 14, whereinthe non-uniform response is due to implanted ions in the resonator film,with a density of the implanted ions increased at the edges of theresonator film.
 16. The acoustic resonator of claim 15, furthercomprising a second set of implanted ions in the top electrode, with ahigher density of the second set of implanted ions at a center of thetop electrode.
 17. The acoustic resonator of claim 5, furthercomprising: circular corrugations on a top surface of the resonatorfilm.
 18. The acoustic resonator of claim 17, wherein the circularcorrugations have a non-uniform spacing defined by a continuous zoneplate.